1. Field of the Invention
The present invention relates to image processing apparatus capable of performing so-called image transformation processing in which uncoded source image information defined in a rectangular area on a plane is projected on a quadrangular area delimited by any four points on the same plane, and more particularly to a device that can perform the transformation with a smaller amount of calculation by employing a point generator.
The image processing apparatus of the invention can apply to a digital display such as a CRT (cathode ray tube), a digital plotter, or a matrix printer.
2. Prior Art
Geometric transformation processing of image information is one of the basic technologies in the field of image processing. Transformation is an important geometric transformation facility for a two-dimensional image because it has the feature of mapping the source image information defined in a rectangular area on the plane to any quadrangular area on the same plane while maintaining the linearity of the image. This allows, for example, providing of free transforming operation of image data on an animation system or the like, application of the so-called texture mapping processing, in which the image is pasted in a plane given in a three-dimensional space, and removal of distortion occurring when an image is entered, which cannot be completely eliminated by expansion/reduction or rotation.
The projective transformation on a plane is determined by four sets of corresponding points. The correspondence between the coordinates of pixels of the source image (x, y), and the coordinates of pixel after the transformation (x', y') is mathematically defined by the following equation using homogenous coordinates. ##EQU1## wherein, x.sub.1 =x, x.sub.2 =y, x.sub.3 =1, x'=x.sub.1 '/x.sub.3 ', y'=x.sub.2 '/x.sub.3 '
FIG. 9(a) (prior art) shows the source image information defined on a point, while FIG. 9(b) (prior art) similarly shows information of an image after transformation (target image) in accordance with the prior art. To perform the transformation for mapping the source image to the target image, the reverse operation of the above-mentioned definition equation (1) is performed, that is, after the mapping from the target image to the source image EQU x=(A.sub.1 x'+B.sub.1 y'+C.sub.1)/(D.sub.1 x'+E.sub.1 y'+F.sub.1) EQU y=(A.sub.2 x'+B.sub.2 y'+C.sub.2)/(D.sub.1 x'+E.sub.1 y'+F.sub.1) (2)
wherein,
A.sub.1 =ds-nq, B.sub.1 =mq-bs, C.sub.1 =bn-dm, PA1 A.sub.2 =np-cs, B.sub.2 =as-mp, C.sub.2 =cm-an, PA1 D.sub.1 =cq-dp, E.sub.1 =bp-aq, F.sub.1 =ad-bc is found, corresponding positions on the source image (p', q' in FIG. 10(a)) (prior art) are found for each pixel of the target image (p', q' in FIG. 10(b)) (prior art) while raster scanning over a rectangular area circumscribing the target image, and then the source image nearest to the positions is made with the values of their pixels (p, q in FIG. 10(a)) the output to the target image. The reason why the mapping reverse to the definition equation (1) is used lies in that the mapping from the source image in the definition equation (1) to the target image may cause gaps in the target image. In such a case, some processing becomes necessary, which is cumbersome.
However, calculation of the above equation requires operations of eight multiplications, eight additions and subtractions, and two divisions. This means that an enormous amount of calculation is required for the transformation processing.
The conventional prior art projective transformation is described in detail in "Computer Image Processing and Recognition" by Ernest L. Hall, Academic Press, pp. 86-88.